In recent years, there have been various formulations of the LOD in terms of localization, interpolation, approximation schemes and applications.
Since we are concerned with the case where storage restrictions may prevent to store explicit solutions of the corrector problems, we focus on the Petrov–Galerkin version of the LOD (PG–LOD) [1]}, which is favorable in this respect.
For further background, we refer to [2]}.
